Tuesday, November 27, 2012

Some time ago, I wrote about why I consider minimum wages unempowering and harmful to the least privileged members of society. I contended that minimum wages shut out from the labor market - a fundamental social institution - those people whose labor is least valuable. It prevents them from exercising what little power they have and perpetuates their disenfranchisement by preventing them from accumulating social and human capital through employment.

I'd like to revisit that topic briefly to better explain why a minimum wage effectively bars the least valuable, least privileged, and least powerful members of society from employment.

The process of establishing wages is effectively a negotiation between employer and employee. In some cases - when the employee's power is checked by the presence of many other potential employees - the employer can set the wage. In other cases - when the employer's power is checked by the presence of many other potential employers - the employee can set the wage. The freer the market, the less power both employee and employer have. All the rest of the time, employee and employer negotiate and arrive at a compromise.

Negotiations end when either the parties reach an agreement, or when one party walks away from the negotiation. The threat of walking away without a deal is a bargaining tactic.

This illuminates the brutal consequences of a minimum wage. In the presence of a minimum wage, the employer cannot offer a wage low enough to make the potential employee a contributing laborer. So the employer walks away from negotiation, leaving the employee out in the cold. The minimum wage effectively bars the least valued members of society from participating in the labor market not by outright exercise of force, but by the conjunction of freedom to walk away from negotiation and conditions on the price of labor.

In a modern, wealthy welfare state, the people most affected by the minimum wage and shut out from labor force participation move from job to job, work for cash, consume very little, and rely on friends, family, charity, and welfare. They're not starving to death, but they are shut out of permanent participation in the labor force. Thus they have difficulty accumulating social and human capital - they're stuck in an effective poverty trap.

So here are two general classes of solutions to this disenfranchisement. One type of solution is to remove the ability of employers to step away from the negotiating table. Mandate that employers take any job applicant and pay them a set wage.

The other type of solution - the type I favor: do away with the minimum wage and replace it with an anti-poverty measure that genuinely empowers the underprivileged, instead of one that merely looks nice to us upper-middle-class folks while silently disenfranchising the poorest, least valuable members of our society.

Saturday, November 17, 2012

I ran across this on Facebook today. It turns out that I have never, in my whole life, experienced a month with below-average temperatures:

The average temperature across land and ocean surfaces during October
was 14.63°C (58.23°F). This is 0.63°C (1.13°F) above the 20th
century average and ties with 2008 as the fifth warmest October on
record. The record warmest October occurred in 2003 and the record
coldest October occurred in 1912. This is the 332nd consecutive month with an above-average temperature.

In other words, for 332 straight months, the average temperature has been above the 20th century average temperature.

This got me thinking about just what the chances of that are. I want to make one simple assumption and then test the hypothesis that global warming is not occurring.

Temperature Deviations

Let's look at temperature deviations. Call the average temperature over the century \(T\). We should think of this as the long-haul temperature. If global warming isn't happening, then this is the "baseline temperature" of the Earth.

Each month, the average temperature doesn't necessarily need to be the same as the long-haul temperature. It might be above or below, depending on whether there's something like El Nino going on, or if the sun is extra-bright, and so on. Either the temperature in that month is above or below the long-run temperature\(T\). Whether or not the temperature is above or below -- one of those two outcomes -- is what we'll focus on.

Here's our one simplifying assumption. The probability of monthly temperature being above or below \(T\) in one month does not depend on whether it was above or below \(T\) in previous months.

This lets us treat monthly temperature as a Bernoulli process. This is a standard piece of finite mathematics which I'll proceed to explain.

Bernoulli Processes

(If you want to get to the meat, skip this section and go to the next one.)

A Bernoulli process is an experiment with the same two outcomes ("success" and "failure") and the same two probabilities (of success, of failure) repeated over and over again. The probabilities don't change from experiment to experiment.

The standard example of a Bernoulli process is flipping a coin over and over again. There are two outcomes each time (heads and tails), and each time the probabilities are the same (\(0.5\)) each).

The usual question in a Bernoulli process is, "What's the probability of getting this many successes in that many trials?" For example, we might ask, "what's the probability of getting \(2\) heads if we flip a coin \(3\) times?" Here's a quick explanation of where the answer comes from. It requires two "black box facts."

We did not specify the order of the heads. So, for example, the outcomes HHT, HTH, THH all qualify as "three heads." Each of these outcomes has the same probability: since the probabilities don't change from experiment to experiment, the experiments are independent. Black-box fact one: The probability of a string of independent outcomes is the product of each outcome's probability. That is, the probability of HHT is the probability of H times the probability of H times the probability of T.

Now to get the probability of two heads (instead of HHT, say) we just have to add up the probabilities of all the different ways we can have two heads in three flips. Each has the same probability, so we just need to multiply that probability by the number of different ways we can get two heads in three flips. Black-box fact two: the number of ways of choosing two of the three flips to be heads (order doesn't matter) is the number \(C(3,2) = 3\).

So the probability of flipping two heads in three tosses is \(3(0.5)^3\).

More generally, the probability of getting \(k\) successes in \(n\) trials (if \(p\) is the probability of success and \(q\) is the probability of failure) is
$$C(n,k)p^kq^{n-k}.$$

Climate as Bernoulli Process

Our climate model is basically a series of coin flips. If the long-haul temperature average isn't changing, then each month, the probability of above-average temperatures is just the same as the probability of below-average temperatures. That is, there's a \(50\%\) chance that either occurs. We want to know the probability of \(332\) above-average temperatures in as many trials.

This just like treating each month as a coin flip. If you flip a coin \(332\) times, what's the chance that you get \(332\) heads in a row?

That is an incredibly small, tiny, vanishing, eensy-weensy, little number. It's on the order of \(10^{-100}\), that is, one in \(10^{100}\). By comparison, there are roughly \(10^{80}\) atoms in the observable universe. So if we gathered all of those atoms into one box, colored one blue and all the rest white, and grabbed one of the atoms while blindfolded, we're billions of times more likely to pick the blue atom than we are to have \(332\) straight months of above-average temperatures.

The tl;dr? If global warming is not happening, and if the temperature each month is independent of the temperature the previous month, then the probability of \(332\) straight positive deviations is a billion trillion times less likely than reaching into a bin of all the atoms in the observable universe and randomly picking the one blue atom. So, global warming is almost certainly happening.

Tuesday, November 13, 2012

I want to make an odd sort of point here. Usually, one thinks of libertarianism as an ideology focused on freedom and "collectivism" as describing an ideology which focuses on restraining freedom for the common good. I want to compare the two and troll around for interesting similarities.

Without being so pedantic as to pull up the dictionary definition, let's identify libertarianism as an ideology of government that holds the following: The best government enforces simple rules of property ownership and contract obligations and restrains coercive behavior (i.e., threat of force to extract negotiating concessions), but does not otherwise constrain behavior. Individual people should be (this ideology holds) free to move about and engage with each other in voluntary interactions.

Libertarian litererary works focus on freedom of action and contrast it with restrictions: Capitalism and Freedom, The Road to Serfdom, Free to Choose, Atlas Shrugged, and so on. The greatest good is achieved when the use of force is restricted to stopping the use of force.

Whence justification for this position? Libertarians are highly suspicious of centralized economic and social coordination for several reasons. These are perhaps the three most cited, aside from a moral imperative that freedom be preserved.

The Hayekian information problem: no single agent can have enough information to successfully coordinate economic activity.

The public choice criticism: Dominant groups subvert central coordination to perpetuate their own dominance.

The efficiency critique: A central planner will require the use of resources to centrally plan, and one large enough to direct the economy will consume a portion of economic resources that could be otherwise used for investment or consumption.

These justifications continue to claim that the well-being of society is higher with minimal government intervention. Libertarianism is a superior ideology, then, for utilitarian reasons: Society as a whole is better off with less central intervention, even if some people are worse off. The better-off people are better off than the worse-off people are worse off.

Collectivism is often thrown around as an epithet by libertarians: "Oh, you're a collectivist." (Apparently, it's often leveled at less dogmatic libertarians as well as at progressives, socialists, or communists --- in one entertaining account, Ludwig von Mises stormed out of a meeting of the Mont Pelerin Society after accusing Milton Friedman of being a socialist.) An ideology may be described as collectivist insofar as it requires the subordination of individual freedom and well-being to the collective good of all of society.

So here's the interesting comparison. Let's grant for a moment the proposal of utilitarian libertarians that a libertarian society is better off than a non-libertarian society. In particular, those who are less well-off than under alternative systems should accept that, for the greater good. Laid-off steel worker? Find a different job - your sacrifice enables lower prices for most people; they are better off than you are worse off. Trained as a vacuum-tube computer punch-card operator? Sorry, obsolete technology - we're all better off using semiconductor computers, except maybe you. Low education? Accept that minimum wage job - you're not capable of offering any more to society, and the resource use in a higher wage is better used elsewhere. If you don't like your circumstances, you should work to improve yourself, not expect society to dump resources into your life so you can be a net drain on it.

What is this, but collectivism? This vision of libertarianism sees humans like ants, and economic order in human society arising as spontaneously as order in an ant colony. To distort that spontaneous order is to hurt the colony as a whole; to embrace that spontaneous order is to embrace the greater good of the colony.

Meanwhile, no ant is intrinsically worthwhile. All ants contribute, and together create great things; but if an ant ceases to be a net contributor, it must change or cease to exist. Same with humans - as a professor of mine once indignantly exclaimed, "Why shouldn't people have to pay the costs they impose on other people?" (Corollary: If someone can't pay, why should they be able to exist?)

It seems to me that this libertarian perspective holds that, sometimes, in service to the greater good of society, people's livelihoods and well-being have to be sacrificed. Society is best off when resources are directed according to free markets, and if that hurts people - so be it; they must have been net drains on society. Thus: libertarianism as collectivism.

Short question: Is this atypical? The question was prompted by this amusing picture:

There are five major exceptions to the pattern: New Mexico, Colorado, Virginia, Florida, and Indiana. With the exception of Indiana, we can predict the changes based on demographics: increases in the Hispanic population, and urbanization around the District of Columbia. But Indiana's demographics haven't significantly changed in the same way - so what's the deal?

So I compared Indiana to its close neighbor Illinois, using the New York Times' data on eachstate. Glancing at county-by-county results, we see broadly similar trends: mostly red, with urban areas and some traditionally Democratic counties blue. The glaring source of difference between Illinois and Indiana is Chicago. I crunched a few numbers (rounding to the nearest thousand and ignoring third-party candidates - those will account for discrepancies of a few percentage points).

Illinois has 20 electoral votes, and just over 5 million votes (5,006,000) were cast in the state. Just under 2 million (1,918,000) of them were cast in Cook County. Obama carried Illinois with 57% of the vote, 2,916,000 votes, while Romney received 43%, or 20,990,000 votes.

Let's suppose that Cook County just suddenly fell into Lake Michigan. What would happen to Illinois' vote totals? Well, instead of 5 million votes, only a handful more than 3 million votes would be cast (much closer to Indiana's 2.6 million total). Removing the Cook County voting from the Obama-Romney statewide totals gives Romney 1,611,000 votes to Obama's 1,477,000 votes. This is an edge of 52% - 48% to Romney (much closer to Indiana's 55%-45%). Romney would get Illinois' electoral votes ... but there wouldn't be 20 anymore. Crude scaling suggests there would be 12 electoral votes (hey, Indiana has 11!).

Neat, huh? If Illinois didn't have Chicago, it would function like Indiana's twin: A state with a couple of mid-sized, moderately dense cities (Indianapolis, Fort Wayne, Evansville, South Bend, ...) in a sea of rural conservative counties. A huge, dense urban area makes the difference between a reliable large Democratic state and a reliable mid-sized Republican state.

What about Ohio, Indiana's other neighbor? It doesn't have any one tremendously huge, dense urban area, nor does it have only a few - instead, it has several large, dense cities spread throughout the state (Cincinnati, Cleveland, Toledo, Columbus, Dayton, Youngstown). The urban/rural tension is finely balanced, so Ohio functions as a swing state.